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3 boxes (ABC) and 3 different ways to arrange the winning box (xyz)
ABC
x 100
y 010
z 001
You pick A box each time and don't switch:
x: host reveals C is not a winner, you don't switch, you WIN
y: host reveals C is not a winner, you don't switch, you LOSE
z: host reveals B is not a winner, you don't switch, you LOSE
You win 1/3 of the time.
You pick A box each time and you switch:
x: host reveals C is not a winner, you switch, you LOSE
y: host reveals C is not a winner, you switch, you WIN
z: host reveals B is not a winner, you switch, you WIN
You win 2/3 of the time.
Total probability: 1/3+2/3=1
Initially picking B or C doesn't effect this result so by switching
you increase your chances to 2/3.
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